This paper proposes an efficient algorithm that not only can narrow down the search domain of face identification but also can reconstruct various 3D objects from a single free-hand line drawing. The algorithm is executed in two stages. In the face identification stage, we generate and classify potential faces into implausible, basis and minimal faces by using geometrical and topological constraints to reduce search space. The proposed algorithm searches the space of minimal faces only to identify actual faces of an object fast. In the object reconstruction stage, we introduce 3D regularities and quadric face regularities to reconstruct 3D object accurately. Furthermore, the proposed method can be applied to a wide scope of general objects containing flat and quadric faces. The experimental results show that the proposed method identifies faces much faster than previous ones and efficiently reconstructs various objects from a single free-hand line drawing.